THE GEODESICS OF A SUB-RIEMANNIAN METRIC ON THE GROUP OF SEMIAFFINE TRANSFORMATIONS OF THE EUCLIDEAN PLANE

被引：2

作者：

Tryamkin, M. V. ^{[1
]}

机构：

[1] Novosibirsk State Univ, Sobolev Inst Math, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2019年 / 60卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

geodesic; sub-Riemannian structure; Lie group;

D O I：

10.1134/S003744661901018X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain the parametrized representations of the geodesics of a left-invariant sub-Riemannian metric on the group of semiaffine transformations of the Euclidean plane. These transformations act as orientation-preserving affine mappings along one axis and as translations along the other.

引用

页码：164 / 177

页数：14

共 50 条

[1] The Geodesics of a Sub-Riemannian Metric on the Group of Semiaffine Transformations of the Euclidean Plane
M. V. Tryamkin
[J]. Siberian Mathematical Journal, 2019, 60 : 164 - 177
[2] The Sub-Riemannian Curvature of Curves in the Group of Semiaffine Transformations of the Euclidean Plane
Tryamkin, M. V.
[J]. MATHEMATICAL NOTES, 2019, 106 (3-4) : 476 - 480
[3] The Sub-Riemannian Curvature of Curves in the Group of Semiaffine Transformations of the Euclidean Plane
M. V. Tryamkin
[J]. Mathematical Notes, 2019, 106 : 476 - 480
[4] Homogeneous Sub-Riemannian Geodesics on a Group of Motions of the Plane
Yu. L. Sachkov
[J]. Differential Equations, 2021, 57 : 1550 - 1554
[5] Homogeneous Sub-Riemannian Geodesics on a Group of Motions of the Plane
Sachkov, Yu L.
[J]. DIFFERENTIAL EQUATIONS, 2021, 57 (11) : 1550 - 1554
[6] Sub-Riemannian Geodesics on the Multidimensional Heisenberg Group
Panzhenskii V.I.
Surina O.P.
[J]. Journal of Mathematical Sciences, 2023, 276 (4) : 541 - 551
[7] Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group SL(2)
V. N. Berestovskiĭ
I. A. Zubareva
[J]. Siberian Mathematical Journal, 2016, 57 : 411 - 424
[8] Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group SL(2)
Berestovskii, V. N.
Zubareva, I. A.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2016, 57 (03) : 411 - 424
[9] Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group SO(3)
V. N. Berestovskiĭ
I. A. Zubareva
[J]. Siberian Mathematical Journal, 2015, 56 : 601 - 611
[10] Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group SO(3)
Berestovskii, V. N.
Zubareva, I. A.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2015, 56 (04) : 601 - 611

← 1 2 3 4 5 →